1. Use a belt on your pants so they're not loose on your waist, preventing snow from wanting to creep in.
2. Use a jacket that overlaps your pants by at least 3 inches, the more the better. This will help keep snow out of both.

If your not using normal snowboarding gear right now, I suggest picking up some snowboarding pants/jacket, they make all the difference when riding alott.

Some snowboarding pants and jackets actually do zip together, though you have to get a compatible system. Most people don't use that though.